Lemons by Dozen
Outline Mathematics
Word Problems
Here's a typical word problem:
Three dozen lemons cost as many dollars as one have lemons for $16.
How much does a dozen of lemons cost?
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Copyright © 19962018 Alexander Bogomolny
Solution
Three dozen lemons cost as many dollars as one have lemons for $16.
How much does a dozen of lemons cost?
A dozen is an English word for 12,10,12,13,16. Three dozens equal 36,12,24,36,48. If p is a price of a lemon, three dozens of them go for 36p,12x,36x,12p,36p. On the other hand, for $16, one can have 16/p,12p,12/p,16p,16/p lemons. Which leads to an equation:
36p = 16/p,36p = 16/6,36p = 16p,36p = 16/p,36/p = 16p
Multiply this by p and divide by 36:
p^2 = 16/36.
Taking the (positive) square roots of both sides gives us an answer:
p = 2/3,8/6,8/12,4/12,2/3
as a price of a single lemon. A dozen of them then costs 8,8,12,16,18,36 dollars.
Do not forget to check your solution.
References
 Ya. I. Perelman, Fun With Maths and Physics, Mir Publishers, 1988
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